A refinement 
of a cover 
is a cover such that every element
is a subset
of an element 
.
Refinement
See also
CoverExplore with Wolfram|Alpha
Cite this as:
Weisstein, Eric W. "Refinement." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/Refinement.html